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A282353 Primes p = x^2 + y^2 such that x + y is a perfect square. 4
41, 53, 313, 317, 337, 353, 373, 397, 457, 577, 1201, 1213, 1381, 1621, 2213, 3461, 3593, 3701, 3761, 4481, 4793, 5021, 5393, 5801, 7321, 7333, 7433, 7541, 7741, 7933, 8081, 8161, 8521, 9181, 9433, 10133, 10601, 11833, 12421, 13933, 14281, 14293, 14321, 14341, 14401, 14461, 14593 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Least prime in which either x&y is k: 577, 53, 13933, 41, 41, 397, 53, 353, 337, etc. - Robert G. Wilson v, Feb 13 2017

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

Prime number 53 is a term because 53 = 2^2 + 7^2 and 2 + 7 = 9 is a perfect square.

MATHEMATICA

fQ[n_] := Block[{x = 1, y, lmt = Sqrt[n/2]}, While[y = Sqrt[n - x^2]; x < lmt && (!IntegerQ@ y || !IntegerQ@ Sqrt[x + y]), x++]; x < lmt]; Select[ Prime @Range@1750, fQ] (* Robert G. Wilson v, Feb 13 2017 *)

PROG

(PARI) is(p)=p%4==1 && isprime(p) && issquare(vecsum(qfbsolve(Qfb(1, 0, 1), p))) \\ Charles R Greathouse IV, Feb 14 2017

CROSSREFS

Cf. A002313, A282381.

Sequence in context: A052032 A176924 A115663 * A118636 A116345 A127333

Adjacent sequences:  A282350 A282351 A282352 * A282354 A282355 A282356

KEYWORD

nonn

AUTHOR

Altug Alkan, Feb 13 2017

STATUS

approved

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Last modified February 23 23:10 EST 2018. Contains 299595 sequences. (Running on oeis4.)